CN115310224A - Method for calculating load-sharing coefficient of planetary gear mechanism - Google Patents
Method for calculating load-sharing coefficient of planetary gear mechanism Download PDFInfo
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Abstract
The invention relates to a method for calculating the load sharing coefficient of a planetary gear mechanism, which comprises the steps of building a finite element model for assembling the planetary gear mechanism; defining the material property of the finite element model, the rigidity of the spring unit and the boundary condition of the finite element model in turn: bolt holes on the split type shell connected with the motor are fixed; defining an initial temperature of the finite element model; applying a load of 1-3; adjusting all parts to an ideal assembly position; determining a 1 st meshing position of the planetary gear mechanism; defining a calculation working condition; carrying out finite element analysis; calculating the load balancing coefficient of the planetary gear mechanism at the 1 st meshing position; adjusting the gear meshing position of the planetary gear mechanism and calculating the load balancing coefficient of the corresponding position; and (4) considering the manufacturing error and the assembly error of the parts, and repeating the steps to calculate the load sharing coefficient of the planetary gear mechanism. The method realizes the high-precision prediction of the load-sharing coefficient of the planetary gear mechanism; the load-sharing coefficient of the planetary gear mechanism is evaluated more reasonably; the calculation speed is improved.
Description
Technical Field
The invention belongs to the technical field of mechanical transmission, and particularly relates to a method for calculating a load balancing coefficient of a planetary gear mechanism.
Background
Planetary gear mechanisms are increasingly applied to transmission systems, such as automatic transmissions, coaxial electric drive bridges, transfer cases and the like, and share load around a sun gear by utilizing a plurality of planetary gears to be uniformly distributed, so that the load born by a single planetary gear is reduced; the characteristics of high internal engagement bearing capacity and large space volume of the inner gear ring are utilized, the radial size and the axial size of the mechanism are reduced, and the compact structure and high bearing capacity are ensured; and the coaxial line of the input shaft and the output shaft is utilized, so that the axial size of the transmission system is shortened. Therefore, the transmission system provided with the planetary gear mechanism has the advantages of small volume, light weight, compact structure, high transmission power, high bearing capacity and the like. In order to fully exert the advantages of the planetary gear mechanism, the load balancing coefficient of the planetary gear mechanism should be as close to 1.0 as possible, but due to the influence of factors such as unavoidable manufacturing errors, installation errors, elastic deformation of parts, temperature and the like, the ideal load balancing coefficient is difficult to achieve, so that the planetary gear in the planetary gear mechanism is inevitably stressed unevenly.
The prior art discloses a new energy automobile planetary gear train uneven load coefficient calculation method, which is characterized in that a finite element method is applied, the contact relation between parts is considered, the stress of a planetary gear under the conditions of manufacturing errors and no manufacturing errors is calculated, and the stress ratio under the two conditions is adopted to evaluate the uniform load condition of the planetary gear. The method has the following disadvantages that 1, the outer surface node of the inner gear ring is restrained, the outer surface of the inner gear ring is assumed to be a rigid surface, the method has the advantages that the calculation speed is high, but the rigidity of an external supporting part in contact with the inner gear ring is not considered, in fact, most of the external supporting part is made of aluminum alloy materials, after the temperature is increased, the thermal expansion amount of the external supporting part is larger than that of the inner gear ring, the thermal expansion amount and the rigidity of the supporting part are both beneficial to the uniform loading of the planetary gear, and therefore the calculated uniform loading coefficient has larger deviation from an actual value; 2. the load balancing performance evaluation is carried out by only calculating the stress of the planetary gear at one moment, and actually, the stress of the planetary gear at different moments is different, and the corresponding load balancing coefficients have larger deviation, so that the evaluation method is unreasonable.
The prior art also discloses a method for calculating the load balancing test load coefficient of a planetary gear box, which applies a test measurement technology, obtains the peak value and the mean value of the peak value of each group of strain gauges by testing the tooth root strain of an inner gear ring, and then evaluates the load balancing condition of a planetary gear by adopting the ratio of the peak value to the peak value. The method has the defects that a uniaxial strain gage or a strain flower is not adopted, which type of strain is adopted for evaluation, and the factors all influence the specific value of the load balancing coefficient of the planetary gear and further influence the evaluation of the load balancing performance of the planetary gear mechanism.
The prior art also discloses a finite element method-based planetary transmission uneven load coefficient calculation, the finite element method is applied, the contact relation between parts is considered, the contact stress of the planetary gear under the two conditions of the position error of the planetary gear and the position error of the planetary gear is calculated, and the contact stress ratio under the two conditions is adopted to evaluate the uniform load condition of the planetary gear. It has the following disadvantages: 1. influence of rigidity of an external supporting part in contact with the inner gear ring is not considered, calculated contact stress deviation is large, and the evaluation effect of the load balancing performance of the planetary gear mechanism is influenced; 2. the contact stress is different when the gears are positioned at different meshing positions, the load sharing coefficient of the planetary gear at one meshing position is only calculated, but not the maximum load sharing coefficient in the rotation process of the planetary gear, and actually, the load sharing coefficients of the planetary gears at different meshing positions are different, so that the load sharing coefficient evaluation method is unreasonable.
Therefore, the load-sharing coefficient of the planetary gear mechanism is effectively evaluated in the early stage of product development so as to judge whether the design of the planetary gear mechanism is reasonable or not and whether the manufacturing process requirements are met or not.
Disclosure of Invention
The invention aims to provide a method for calculating the load-sharing coefficient of a planetary gear mechanism, which aims to solve the problem of judging whether the design of the planetary gear mechanism is reasonable and whether the manufacturing process requirements are met.
The purpose of the invention is realized by the following technical scheme:
a load sharing coefficient calculation method of a planetary gear mechanism comprises the following steps:
s1, building a finite element model for assembling a planetary gear mechanism:
respectively carrying out entity grid division on a sun gear, a planet carrier, an inner gear ring, a shell and an inner ring and an outer ring of a bearing in a planetary gear mechanism, and defining contact relations among contact parts to assemble the contact parts together;
s2, defining the material attribute of the finite element model:
defining the elastic modulus E, poisson ratio mu, material density rho and thermal expansion coefficient alpha of each part finite element model material;
s3, defining the rigidity K of the spring unit in the step S1:
s4, defining boundary conditions of the finite element model: bolt holes on the split type shell connected with the motor are fixed;
s5, defining the initial temperature of the finite element model: applying initial temperature to all the part finite element models in the step S1;
s6, applied load 1: the load 1 is a temperature load, namely, a high-temperature load is applied to finite element models of all parts in the step S1;
s7, applied load 2: the load 2 is torque M on the input shaft and is applied to the input shaft by virtue of an RBE3 unit, the RBE3 unit selects the central point of the end surface of the input shaft away from one end of the sun gear from a point, a main point selects a node on the end surface of the input shaft away from one end of the sun gear, and M is applied to the RBE3 unit from point;
s8, applied load 3: the load 3 is a centrifugal force, and the centrifugal forces of all rotating parts in the step S1 are specifically shown in calculation formulas (3) - (9);
w 2 ＝2πn 2 (4)
in equations (3) to (4): f 2 Is the grid cell centrifugal force of the sun gear; m is 2 Is the grid cell mass of the sun gear; r is a radical of hydrogen 2 The rotation radius of the grid unit of the sun wheel; w is a 2 Is the angular velocity of the sun gear; n is 2 The rotational speed of the sun gear;
w 3 ＝2πn 3 (6)
in formulas (5) to (7): f 3 A grid cell centrifugal force for the planet carrier; m is 3 The grid cell mass of the planet carrier; r is 3 The mesh unit rotating radius of the planet carrier; w is a 3 Is the angular velocity of the planet carrier; n is 3 The rotational speed of the planet carrier; z is a radical of 2 The number of sun gear teeth; z is a radical of R The number of teeth of the inner gear ring;
in equations (8) to (9): f 4 A grid cell centrifugal force that is a planetary gear; m is 4 A grid cell mass for the planetary gear; r is a radical of hydrogen 4 The revolution rotation radius of the grid unit of the planetary gear; w is a 4 Is the revolution angular velocity, w, of the planetary gear 4 ＝w 3 ；r 41 The mesh unit autorotation radius of the planet gear; w is a 41 Is the rotational angular velocity of the planetary gear; r 4 The revolution radius of the central line of the planetary gear; r is 42 Is the pitch circle radius of the planet gear; r is 22 Is the pitch circle radius of the sun gear;
s9, adjusting all parts to an ideal assembly position:
adjusting each part in the step S1 to an ideal assembly position without considering the manufacturing error and the assembly error of the part;
s10, determining the 1 st meshing position of the planetary gear mechanism: rotating the planetary gear to any rotational symmetry plane position of the inner gear ring to serve as the 1 st meshing position of the planetary gear mechanism so as to calculate the load balancing coefficient of the planetary gear mechanism at the moment and evaluate the reasonability of the structural design of the parts;
s11, defining a calculation working condition: the calculation condition consists of the boundary condition in the step S4, the initial temperature in the step S5, the load 1 in the step S6, the load 2 in the step S7 and the load 3 in the step S8;
s12, carrying out finite element analysis: according to the calculation condition defined in the step S11, the tangential force of the spring unit of the simulated needle roller in the revolution direction of the planetary gear is calculated in consideration of geometric nonlinearity;
s13, calculating the load sharing coefficient of the planetary gear mechanism at the 1 st meshing position:
multiplying the tangential force of each spring unit of each simulated rolling needle in the revolution direction of the planetary gear by the revolution radius of the supported planetary gear to obtain the torque transmitted by the planetary gear shaft, and taking the ratio of the maximum value of the torque to the average value of all the torques as the load-sharing coefficient of the planetary gear mechanism at the meshing position 1, specifically referring to a calculation formula (10);
in equation (10): s is 1 Is the load-sharing coefficient; f. of j The tangential force of the jth spring unit for simulating the roller pin along the revolution direction of the planetary gear; r is 4j The revolution radius of the planet gear supported by the jth spring unit;
s14, adjusting the gear meshing position of the planetary gear mechanism and calculating the load balancing coefficient of the corresponding position:
the planet gears are sequentially rotated to other non-rotational symmetry plane positions, simultaneously the sun gear and the planet carrier are rotated according to the speed ratio to obtain the 2 nd, the 3 rd, \8230the8230and the x-th meshing positions of the planet gear mechanism, the steps S11 to S13 are respectively repeated at each position, and the load-sharing coefficient S of the corresponding meshing position is calculated 2 、s 3 、……s x (ii) a Get s 1 、s 2 、s 3 、……s x The medium maximum value is used as the load balancing coefficient of the planetary gear mechanism;
and S15, considering manufacturing errors and assembly errors of the parts, and repeating the steps S11 to S14 to calculate the load sharing coefficient of the planetary gear mechanism.
Further, in step S1, a spring unit is used for simplified modeling of a bearing rolling element, for a bearing with an outer ring and an inner ring, nodes at two ends of the spring unit for simulating the rolling element are respectively connected to slave points of two RBE3 units, the two slave points are located on a geometric center line of the bearing, the slave point of one RBE3 unit selects a geometric center of an outer ring raceway, the master point selects a node on the outer ring raceway, the slave point of the other RBE3 unit selects a geometric center of an inner ring raceway, and the master point selects a node on the inner ring raceway; for a needle bearing without an outer ring and an inner ring, nodes at two ends of a spring unit simulating a needle roller are also connected to two RBE3 unit slave points, the two slave points are positioned on a geometric central line of the needle bearing, one slave point of one RBE3 unit selects one point on the central line of the needle bearing, a master point selects a grid node of a planetary gear part in contact with the outer diameter side of the needle bearing, the other slave point of the other RBE3 unit selects the other point on the central line of the needle bearing, and the master point selects a grid node of a planetary gear shaft part in contact with the inner diameter side of the needle bearing; the number of spring units is equal to the number of bearings.
In step S1, the bearing and the housing and the supported member are in zero-clearance fit regardless of interference.
Further, step S3, the spring unit stiffness K represents the comprehensive stiffness of all rolling elements in a bearing, and the specific acquisition method is subdivided into steps S3-1 to S3-8;
s3-1, establishing a finite element model of a single rolling body: the method comprises the steps of carrying out meshing on three parts, namely a rolling body, an upper flat plate and a lower flat plate, wherein meshes of contact positions need to be finely divided so as to improve load transfer precision and deformation calculation precision; the upper flat plate and the lower flat plate are assumed to be rigid bodies so as to obtain the rigidity of a single rolling body; the parts are assembled together by defining a contact relation;
s3-2, defining the material property of the finite element model of the single rolling body: defining the elastic modulus E and the Poisson ratio mu of the rolling body;
s3-3, defining finite element model boundary conditions of a single rolling body: the boundary conditions include two types, namely, the lower flat plate is completely restrained and fixed; secondly, constraining all the degrees of freedom of the upper flat plate except the normal degree of freedom of the upper flat plate so as to ensure that the upper flat plate can only move along the normal direction of the upper flat plate;
s3-4, applying load F borne by single rolling body 1 ：F 1 Acting on the upper plate, F 1 The rolling bodies are compressed and deformed along the normal direction of the upper flat plate;
s3-5, defining the calculation condition of a single rolling body: the calculated operating conditions include boundary conditions in S3-3 and load F in S3-4 1 ；
S3-6, carrying out finite element analysis on the single rolling body: calculating the compression deformation X of the rolling body according to the calculation conditions defined in the step S3-5 1 Which is equal to the load F 1 The distance of the action point moving along the normal direction of the upper flat plate;
s3-7, calculating the rigidity K of a single rolling body 1 : rigidity K 1 See concretely the calculation formula (1);
s3-8, calculating the rigidity K of the spring unit: k is equal to the comprehensive rigidity of all rolling bodies in one bearing, and particularly, the calculation formula (2) is shown;
K＝K 1 ×(COSθ 1 +COSθ 2 +……+COSθ i ) (2)
in the formula, theta i The angle of the ith rolling body relative to the 1 st rolling body is taken as the center of a circle at the intersection point of planes formed by the central line of the bearing and the central points of all the rolling bodies, the 1 st ball can be any ball in the bearing, and theta is the angle between the ith rolling body and the 1 st rolling body 1 ＝0，θ i ＜90。
Furthermore, the stiffness of the spring unit needs to be defined in the radial direction of the bearing by means of a cylindrical coordinate system, the origin of the cylindrical coordinate system is located on the central line of the bearing, the r axis of the coordinate system is along the radial direction of the bearing, the z axis is along the central line of the bearing, and t is determined by the r axis and the z axis according to the right-hand rule.
Further, in step S5, the initial temperature is defined as room temperature.
Further, in step S6, the high temperature load applied to all the finite element models of the components in step S1 is the same, and the temperature value is greater than the normal operating temperature value of the planetary gear mechanism.
Further, in step S7, the torque M is the maximum design input torque of the planetary gear mechanism.
Further, in step S10 and step S14, the meshing positions included are uniformly distributed between two adjacent symmetry planes of the ring gear.
Further, in step S15, the manufacturing error is equivalent to a position error of one of the planetary gear central lines along the planetary gear revolution tangential direction, that is, an equivalent tangential position error, specifically, see calculation formula (11); the assembly error is equivalent to a position error of one of the planetary gear central lines along the revolution radius direction of the planetary gears, namely an equivalent radial position error, which is specifically shown in a calculation formula (12); the manufacturing error and the assembly error are applied to the planetary gear by adopting the comprehensive equivalent position error, the comprehensive equivalent position error is calculated according to a formula (13), and specifically, the distance of the planetary gear deviating from an ideal assembly position by the comprehensive equivalent position error is used for evaluating whether the design of the planetary gear mechanism meets the requirements of the manufacturing process;
in equations (11) to (13): Δ w 1 Is an equivalent tangential position error; p is a radical of formula 1 Is the sun gear eccentricity error; p is a radical of 2 The eccentric error of the planet wheel; p is a radical of formula 3 The eccentric error of the inner gear ring is adopted; p is a radical of 4 The eccentric error of the planet carrier; p is a radical of 5 The eccentric error of the shaft hole of the planet gear shaft; theta is a gear pressure angle; Δ w 2 Is the equivalent radial position error; a is a 1 Assembling errors for the sun gear; a is a 2 Assembling errors for the planet gears; a is a 3 The assembly error of the inner gear ring; a is a 4 Assembling errors for the planet carrier; a is 5 The assembly error of the shaft hole of the planet gear shaft; Δ w is the integrated equivalent position error.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention establishes a finite element model of the load-sharing coefficient of a fully flexible planetary gear mechanism comprising a sun gear, a planetary gear, a planet carrier, an inner gear ring, a shell and a bearing, and the finite element model is closer to a physical prototype; the constraint is applied to a split type shell bolt hole connected with the motor, the split type shell bolt hole is far away from the concerned planetary gear mechanism, and the influence on the stress of the planetary gear is reduced to the minimum; the loads comprise torque loads, centrifugal loads during revolution and autogyration and temperature loads, the consideration is more comprehensive, the condition of the planetary gear mechanism is ensured to be more consistent with the real condition, and the measures effectively realize the high-precision prediction of the load-sharing coefficient of the planetary gear mechanism;
2. the invention multiplies the tangential force transmitted by the planet gear by the revolution radius of the planet gear to obtain the torque transmitted by the planet gear, and introduces the influence of manufacturing errors and assembly errors on the transmitted torque through the revolution radius change of the planet gear; the ratio of the torque transmitted by one of the planetary gears to the average value of the torque transmitted by all the planetary gears is used for carrying out load balancing evaluation on the planetary gear mechanism, and the condition of torque reduction of the planetary gears caused by friction in the torque transmission process is considered, so that the load balancing coefficient of the planetary gear mechanism is more reasonable when the planetary gears are used for transmitting the torque;
3. compared with the prior art that the load-sharing coefficient of the planetary gear mechanism is evaluated by adopting the tooth root stress, the tooth root strain and the tooth surface contact pressure, the influence of microstructures such as a tooth root local structure, a tooth surface microstructure modification and the like can be effectively ignored when the torque transmitted by the planetary gear is evaluated, the calculated load-sharing coefficient is more reasonable, the planetary gear mechanism can be evaluated more reasonably, and unnecessary structural change is reduced;
4. according to the invention, the bearing rolling body is simulated by adopting the spring unit, and the real supporting rigidity is given, so that the scale of a finite element model is effectively reduced, and the calculation speed is increased.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
FIGS. 1-6 are schematic views of a planetary gear mechanism;
fig. 7 is a schematic view of a bearing outer race RBE3 unit;
fig. 8 is a schematic view of a bearing inner race RBE3 unit;
FIG. 9 is a schematic view of the RBE3 unit in the portion of the planetary gear in contact with the outer diameter side of the needle bearing;
FIG. 10 is a schematic view of the RBE3 unit at the portion of the planet pin that contacts the inner diameter side of the needle bearing;
FIG. 11 is a schematic diagram of a finite element analysis model of the rigidity of a single rolling body;
FIG. 12 is a schematic diagram for assisting calculation of comprehensive rigidity of all rolling bodies of a ball bearing;
FIG. 13 is a centrifugal force calculation aid diagram;
FIG. 14 is a schematic view of the planetary gear mechanism meshing position;
FIG. 15 is a schematic illustration of the load sharing factor of the planetary gear mechanism with the parts in the planetary gear mechanism in the theoretical assembled position;
FIG. 16 is a schematic illustration of the application of manufacturing and assembly tolerances;
fig. 17 is a schematic view of the load share factor of the planetary gear mechanism in consideration of manufacturing errors and assembly errors.
Detailed Description
The invention is further illustrated by the following examples:
the present invention will be described in further detail with reference to the accompanying drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not to be construed as limiting the invention. It should be further noted that, for the convenience of description, only some of the structures related to the present invention are shown in the drawings, not all of the structures.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures. Meanwhile, in the description of the present invention, the terms "first", "second", and the like are used only for distinguishing the description, and are not construed as indicating or implying relative importance.
The invention discloses a method for calculating the load sharing coefficient of a planetary gear mechanism, which comprises the following steps:
s1, building a finite element model for assembling a planetary gear mechanism:
the sun gear, the planet carrier, the inner gear ring, the shell and the inner ring and the outer ring of the bearing in the planetary gear mechanism are respectively subjected to entity meshing division, and contact parts are defined to be in contact relation and assembled together.
As shown in fig. 1 to 4, the sun gear 1001 and the input shaft 1002 are of an integral structure, and are divided into a solid grid; the planetary gears comprise 3 primary reduction planetary gears (a primary reduction planetary gear I2001, a primary reduction planetary gear II 2003 and a primary reduction planetary gear III 2005) and 3 secondary reduction planetary gears (a secondary reduction planetary gear I2002, a secondary reduction planetary gear II 2004 and a secondary reduction planetary gear III 2006), which are divided into solid grids, and the primary reduction gear I2001 and the secondary reduction gear I2002, the primary reduction gear II 2003 and the secondary reduction gear II 2004 and the primary reduction gear III 2005 and the secondary reduction gear III 2006 are respectively connected together through common nodes to simulate an interference assembly relationship; the planet carrier comprises 3 planet gear shafts (a planet gear shaft I3001, a planet gear shaft II 3002 and a planet gear shaft III 3003) and a differential case 4000, which are divided into solid grids, and the planet gear shafts are assembled with the differential case 4000 respectively through defining contact relation; the shell for supporting the planetary gear mechanism comprises two split shells (a shell I5001 and a shell II 5002) which are divided into solid grids, and the two split shells are connected together through a rigid body unit RBE2 defined at the position of a bolt hole 5003; the ring gear 7001 is located inside the shell II 5002 and is a floating part and needs to be divided into a solid grid, and the ring gear 7001 and the shell II 5002 are assembled together through a defined contact relation.
As shown in fig. 5 and 6, the bearings include a bearing i 6001 for supporting the input shaft, a bearing ii 6002, a bearing iii 6003 for supporting the differential case, a ball bearing iv 6004, a needle bearing i 6005 for supporting the planetary gear, a needle bearing ii 6006, and a needle bearing iii 6007, wherein the outer ring and the inner ring of the bearing i 6001, the bearing ii 6002, the bearing iii 6003, and the ball bearing iv 6004 are divided into solid meshes; in order to improve the calculation efficiency without influencing the calculation accuracy, the rolling elements are simulated by spring units, and the Abaqus software corresponds to joint units. As shown in fig. 7 and 8, taking a bearing 6001 as an example, the bearing has an outer ring and an inner ring, nodes at two ends of a spring unit simulating a rolling element are respectively connected to slave points of two RBE3 units, the two slave points are located on a geometric center line 6008 of the bearing 6001, the slave point of one RBE3 unit 6009 selects a geometric center 6010 of the outer ring raceway 6011, the master point selects a node on the outer ring raceway 6010, the slave point of the other RBE3 unit 6012 selects a geometric center 6013 of the inner ring raceway 6014, and the master point selects a node on the inner ring raceway 6013.
As shown in fig. 9 and 10, taking a needle bearing i 6005 as an example, the bearing has no outer ring and inner ring, two end nodes of a spring unit simulating needle rollers are also connected to two RBE3 unit slave points, the two slave points are located on the geometric center line of the needle bearing i 6005, one slave point of one RBE3 unit 6015 selects one point 6016 on the center line of the needle bearing i 6005, the master point selects a grid node at the position contacting with the outer diameter side of the needle bearing at the planetary gear portion 6017, the other slave point of the other RBE3 unit 6018 selects the other point 6019 on the center line of the needle bearing i 6005, and the master point selects a grid node at the position contacting with the inner diameter side of the needle bearing at the planetary gear portion 6020; the number of spring units in the embodiment is 7, which is equal to the number of bearings.
Interference is not considered between the bearing I6001, the bearing II 6002, the bearing III 6003 and the ball bearing IV 6004 and the shell and between the supported parts, and the interference is zero clearance fit.
S2, defining the material attribute of the finite element model:
defining the elastic modulus E, poisson ratio mu, material density rho and thermal expansion coefficient alpha of finite element model materials of each part;
wherein, the materials of the shell I5001 and the shell II 5002 are aluminum alloy AlSi9Cu3, E =71000MPa, mu =0.33, rho =2700kg/m 3 α =0.0000212/° c; the differential case 4000 is made of nodular cast iron QT600, E =17500MPa, mu =0.3, rho =7090kg/m 3 α =0.0000118/° c; the others are ferroalloys, E =210000MPa, mu =0.3, rho =7800kg/m 3 、α＝0.0000127/℃。
S3, defining the rigidity K of the spring unit in the step S1:
the spring unit stiffness K represents the comprehensive stiffness of all rolling bodies in a bearing, the specific acquisition method is subdivided into steps S3-1 to S3-8, and the calculation process and the application process of the K are described by taking the ball bearing IV 6004 as an example.
S3-1, establishing a finite element model of a single rolling body: as shown in fig. 11, including meshing of three components of the ball 6021, the upper plate 6022, and the lower plate 6023, in which the mesh of the contact position needs to be finely divided to improve the load transfer accuracy and the deformation calculation accuracy; the upper plate 6022 and the lower plate 6023 are assumed to be rigid bodies to obtain the rigidity of a simple sphere; the parts are assembled together by defining a contact relationship.
S3-2, defining the material property of the finite element model of the single rolling body: elastic modulus E =210000MPa and poisson ratio μ =0.3 of the ball 6021 are defined.
S3-3, defining finite element model boundary conditions of a single rolling body: the boundary conditions comprise two types, namely, the lower surface of the lower flat plate 6023 is completely restrained and fixed; secondly, the upper flat plate 6022 is constrained to move along the normal direction by all degrees of freedom except the normal degree of freedom thereof.
S3-4, applying load F borne by single rolling body 1 : as shown in FIG. 11, F 1 Acting on the upper plate 6022, F 1 Compressive deformation of the ball in the direction normal to the upper plate 6022, F 1 ＝5000N。
S3-5, defining the calculation condition of a single rolling body: the calculated operating conditions include boundary conditions in S3-3 and load F in S3-4 1 。
S3-6, carrying out finite element analysis on the single rolling body: calculating the compression deformation X of the ball according to the calculation conditions defined in the step S3-5 1 Which is equal to the load F 1 Distance, X, that the point of action moves normal to the upper plate 6022 1 ＝0.08652mm。
S3-7, calculating the rigidity K of single rolling body 1 : rigidity K 1 See formula (1), calculated K 1 ＝57790N/mm；
S3-8, calculating the rigidity K of the spring unit: k is equal to the comprehensive rigidity of all balls in one bearing, and is shown in a calculation formula (2);
K＝K 1 ×(COSθ 1 +COSθ 2 +……+COSθ i ) (2)
in the formula, theta i The angle of the ith ball relative to the 1 st ball is determined by taking the intersection point of the central line of the ball bearing and the plane where the centers of all the balls are located as the center of a circle,the 1 st ball may be any ball in the bearing, θ 1 ＝0，θ i ＜90°。
As shown in fig. 12, the ball bearing iv 6004 comprises 9 balls, the plane formed by the central line of the ball bearing iv 6004 and the centers of all the balls intersects at the center 6024, and the angle between two adjacent balls is 40 °, i =5; the 1 st ball is located at the bottom end of the bearing, theta 1 ＝0；θ 2 ＝θ 3 ＝40°，θ 4 ＝θ 5 =80 °, will K 1 、θ i Substituting the specific value into the formula (2), and calculating the spring stiffness K =166400N/mm; as shown in fig. 12, the spring unit stiffness K needs to be defined in the bearing radial direction by means of a cylindrical coordinate system 6025, with the origin of the cylindrical coordinate system located at the center 6024, the r-axis of the coordinate system along the bearing radial direction, the z-axis along the bearing center line direction, and t determined by the r-axis and the z-axis according to the right-hand rule.
And (3) repeating the steps S3-1 to S3-8, calculating the comprehensive stiffness of the rolling bodies of other bearings, and endowing corresponding spring units with the comprehensive stiffness K =217656N/mm of the rolling body of the bearing I6001, the comprehensive stiffness K =166400N/mm of the rolling body of the bearing II 6002, the comprehensive stiffness K =386660N/mm of the rolling body of the bearing III 6003, and the comprehensive stiffness K =10344668N/mm of the rolling bodies of the needle bearing I6005, the needle bearing II 6006 and the needle bearing III 6007.
S4, defining boundary conditions of the finite element model: bolt holes 5004 in the split housing connected to the motor are fixed.
S5, defining the initial temperature of the finite element model: an initial temperature, i.e. 25 ℃ at room temperature, is applied to the finite element model of all the parts in step S1.
S6, applied load 1: the load 1 is a temperature load, that is, a high temperature load is applied to all the part finite element models in step S1, and the high temperature loads applied to all the part finite element models are the same and equal to 120 ℃.
S7, applied load 2: load 2 is the torque M on the input shaft 1002 equal to the maximum design input torque 300Nm for the planetary gear mechanism, which is applied to the input shaft by the RBE3 unit 1003, which selects the input shaft end face center point 1004 remote from the sun gear end, the main point selects the node on the input shaft end face 1005 remote from the sun gear end, and M is applied to the RBE3 unit slave point, as shown in fig. 5.
S8, applied load 3: the load 3 is a centrifugal force, specifically comprises the centrifugal forces of all rotating parts in the step S1, and is specifically shown in calculation formulas (3) - (9);
w 2 ＝2πn 2 (4)
in equations (3) to (4): f 2 The grid cell centrifugal force for the sun gear and the input shaft; m is 2 The grid cell mass for the sun gear and input shaft; r is a radical of hydrogen 2 The grid cell rotation radius for the sun gear and the input shaft; w is a 2 Angular velocities of the sun gear and the input shaft; n is 2 The rotational speed of the sun gear and the input shaft;
w 3 ＝2πn 3 (6)
in formulas (5) to (7): f 3 A grid cell centrifugal force for the planet carrier; m is a unit of 3 The grid cell mass of the planet carrier; r is 3 The mesh unit rotating radius of the planet carrier; w is a 3 Is the angular velocity of the planet carrier; n is 3 The rotational speed of the planet carrier; z is a radical of 2 The number of sun gear teeth; z is a radical of R The number of teeth of the inner gear ring;
in equations (8) to (9): f 4 A grid cell centrifugal force that is a planetary gear; m is 4 A grid cell mass for the planetary gear; r is 4 The revolution rotation radius of the grid unit of the planetary gear; w is a 4 Is the revolution angular velocity, w, of the planetary gear 4 ＝w 3 ；r 41 The mesh unit autorotation radius of the planet gear; w is a 41 Is the rotational angular velocity of the planetary gear; r 4 The revolution radius of the central line of the planetary gear; r is 42 The pitch circle radius of the planet gear; r is 22 The pitch circle radius of the sun gear.
As shown in FIG. 13, a unit s on the sun gear u For example, the centrifugal force calculation process, the centrifugal force load calculation process of units on other units and other parts and the unit s u The same; unit s u Mass m 2 ＝3.14×10 -15 kg, distance r from the geometric center line 6008 of the rotary shaft bearing I6001 2 ＝24.6×10 -3 m, angular velocity w around centerline 6008 2 ＝2×π×n 2 60/1675.5/s, the centrifugal force can be obtained from the equations (3) to (4)
S9, adjusting all parts to an ideal assembly position:
the parts are adjusted to the desired assembly positions in step S1 regardless of manufacturing errors and assembly errors of the parts.
S10, determining the 1 st meshing position of the planetary gear mechanism: as shown in fig. 14, the two-stage reduction planetary gear 2002 is rotated to a position on any rotational symmetry plane 7002 of the ring gear 7001 as the 1 st engagement position of the planetary gear mechanism to calculate the load sharing factor of the planetary gear mechanism at that time, and the reasonableness of the structural design of the parts is evaluated.
S11, defining a calculation working condition: the calculated operating conditions consist of the boundary conditions in step S4, the initial temperature in step S5, the load 1 in step S6, the load 2 in step S7, and the load 3 in step S8.
S12, carrying out finite element analysis: according to the calculation condition defined in step S11, the tangential forces of the spring units simulating the needle rollers 6005, 6006, 6007 in the revolving direction of the secondary reduction planetary gear i 2002, the secondary reduction planetary gear ii 2004, iii 2006 are calculated in consideration of geometric nonlinearity.
S13, calculating the load sharing coefficient of the planetary gear mechanism at the 1 st meshing position:
the tangential force of the spring unit of each simulated rolling needle in the revolution direction of the planetary gear is multiplied by the revolution radius of the supported planetary gear, so that the torque transmitted by the planetary gear shaft is obtained, and the ratio of the maximum value of the torque to the average value of all the torques is taken as the load-sharing coefficient of the planetary gear mechanism at the meshing position 1, which is shown in a formula (10);
in equation (10): s 1 Is the load-sharing coefficient; f. of j The tangential force of the jth spring unit simulating the roller pin along the revolution direction of the planetary gear; r 4j Is the revolution radius of the planetary gear supported by the jth spring unit.
In this example, f 1 ＝8660N、f 2 ＝9061N、f 3 ＝9497N、R 41 ＝R 42 ＝R 43 =75mm, s is obtained from equation (10) 1 ＝1.047。
S14, adjusting the gear meshing position of the planetary gear mechanism and calculating the load balancing coefficient of the corresponding position:
as shown in FIG. 14, a two-stage reduction planetary gear I2002 is sequentially rotated to positions 7003, 7004, 8230, 8230307037 along an inner gear ring 7001, all the positions are uniformly distributed between a symmetry plane 7002 and a symmetry plane 7038, and simultaneously a sun gear, a planet carrier and other planetary gears are rotated according to a speed ratio to obtain the 2 nd, 3 rd, 8230, 8230and 36 th meshing positions of the planetary gear mechanism, steps S11 to S13 are respectively repeated at each position, and the load sharing coefficient S of the corresponding meshing position is calculated 2 、s 3 、……s 36 (ii) a Get s 1 、s 2 、s 3 、……s 36 The medium maximum value is used as the load-sharing coefficient of the planetary gear mechanism.
The load balancing coefficients of the two-stage reduction driven gear I2002, the two-stage reduction driven gear II 2004 and the two-stage reduction driven gear III 2006 corresponding to different meshing positions are shown in fig. 15, and it can be seen from the figure that the highest points of the three curves are basically close to each other and are respectively 1.068, 1.068 and 1.070, so that the maximum load balancing coefficient is 1.070 when each part of the planetary gear mechanism is in the ideal assembly position in the step S9, and is relatively close to 1, and accordingly, the structural design of the part is judged to be reasonable.
S15, considering manufacturing errors and assembly errors of parts, repeating the steps S11 to S14 to calculate the load sharing coefficient of the planetary gear mechanism:
the manufacturing error is equivalent to a position error of the central line of one of the planet gears along the revolution tangent direction of the planet gears, namely an equivalent tangential position error, and particularly see a calculation formula (11); the assembly error is equivalent to a position error of one of the planetary gear central lines along the revolution radius direction of the planetary gears, namely an equivalent radial position error, which is specifically shown in a calculation formula (12); the manufacturing error and the assembly error are applied to the planetary gear by adopting the comprehensive equivalent position error, the comprehensive equivalent position error is calculated according to a formula (13), and specifically, the distance of the planetary gear deviating from an ideal assembly position by the comprehensive equivalent position error is used for evaluating whether the design of the planetary gear mechanism meets the requirements of the manufacturing process;
in equations (11) to (13): Δ w 1 Is the equivalent tangential position error; p is a radical of formula 1 Is the sun gear eccentricity error; p is a radical of 2 The eccentric error of the planet wheel; p is a radical of 3 The eccentric error of the inner gear ring is adopted; p is a radical of formula 4 The eccentric error of the planet carrier; p is a radical of 5 The eccentric error of the shaft hole of the planet gear shaft; theta is the gear pressure angle; Δ w 2 Is the equivalent radial position error; a is 1 An assembly error for the sun gear; a is 2 Assembling errors for the planet gears; a is 3 The assembly error of the inner gear ring; a is 4 Assembly errors for the planet carrier; a is 5 The assembly error of the shaft hole of the planet gear shaft; Δ w is the integrated equivalent position error.
In the embodiment, the manufacturing error and the assembly error of the parts are shown in table 1, the specific numerical value is substituted into the formulas (11) to (13) to calculate the delta w 1 ＝0.051mm、Δw 2 =0.052mm, Δ w =0.073mm, and the corresponding application process is as shown in fig. 16, and the primary planetary gear 2001 and the secondary planetary gear 2002 are shifted in the same direction by the same distance on the basis of step S9, specifically, the two gears are shifted by Δ w in the opposite direction of revolution 1 Moving Δ w in the direction of the inner gear ring 7001 along the radial direction of the inner gear ring 7001 2 。
TABLE 1 error values for components
The steps 11 to 14 are repeated to calculate the load sharing coefficient of the planetary gear mechanism, the load sharing coefficients of the corresponding second-stage reduction driven gear I2002, the second-stage reduction driven gear II 2004 and the second-stage reduction driven gear III 2006 at different meshing positions are shown in fig. 17, and it can be seen from the figure that the highest points of the two curves corresponding to the second-stage reduction driven gear II 2004 and the second-stage reduction driven gear III 2006 are basically close to each other and are respectively 1.208 and 1.275, and the highest point of the curve corresponding to the second-stage reduction driven gear I2002 is 0.773 which is smaller, so that after manufacturing errors and assembly errors are considered by parts of the planetary gear mechanism, the maximum load sharing coefficient of the planetary gear mechanism is 1.275, the numerical value is larger, and the floating design of the annular gear should be optimized subsequently to reduce the maximum load sharing coefficient of the planetary gear mechanism.
The invention is more consistent with the physical conditions from the modeling of the planetary gear mechanism to the definition of boundary conditions and load conditions; the load-sharing coefficient of the planetary gear mechanism is evaluated by adopting torque transmitted by a planetary gear, the torque belongs to a macroscopic quantity, the influence of micro-modification of a gear tooth surface is small, and the evaluation of the adopted torque is more reasonable than the evaluation of micro-parameters such as tooth root stress, tooth surface contact stress and the like in the prior art; the spring unit is adopted to simulate the rigidity of the bearing rolling element, so that the finite element calculation scale of the planetary gear mechanism is effectively reduced while the rigidity of the rolling element is accurately simulated.
It is to be noted that the foregoing is only illustrative of the preferred embodiments of the present invention and the technical principles employed. It will be understood by those skilled in the art that the present invention is not limited to the particular embodiments described herein, but is capable of various obvious changes, rearrangements and substitutions as will now become apparent to those skilled in the art without departing from the scope of the invention. Therefore, although the present invention has been described in some detail by the above embodiments, the invention is not limited to the above embodiments, and may include other equivalent embodiments without departing from the spirit of the invention, and the scope of the invention is determined by the scope of the appended claims.
Claims (10)
1. A method for calculating the load sharing coefficient of a planetary gear mechanism is characterized by comprising the following steps:
s1, building a finite element model for assembling a planetary gear mechanism:
respectively carrying out entity grid division on a sun gear, a planetary gear, a planet carrier, an inner gear ring, a shell and an inner ring and an outer ring of a bearing in the planetary gear mechanism, and defining contact relation among contact parts to assemble the contact parts together;
s2, defining the material properties of the finite element model:
defining the elastic modulus E, poisson ratio mu, material density rho and thermal expansion coefficient alpha of finite element model materials of each part;
s3, defining the rigidity K of the spring unit in the step S1:
s4, defining boundary conditions of the finite element model: bolt holes on the split type shell connected with the motor are fixed;
s5, defining the initial temperature of the finite element model: applying initial temperature to all the part finite element models in the step S1;
s6, applied load 1: the load 1 is a temperature load, namely a high-temperature load is applied to all the part finite element models in the step S1;
s7, applied load 2: the load 2 is torque M on the input shaft and is applied to the input shaft by virtue of an RBE3 unit, the RBE3 unit selects the central point of the end surface of the input shaft far away from one end of the sun gear from a point, a main point selects a node on the end surface of the input shaft far away from one end of the sun gear, and M is applied to the RBE3 unit from a point;
s8, applied load 3: the load 3 is a centrifugal force, and the centrifugal forces of all rotating parts in the step S1 are specifically shown in calculation formulas (3) - (9);
w 2 ＝2πn 2 (4)
in equations (3) to (4): f 2 A grid cell centrifugal force for the sun gear; m is 2 Is the grid cell mass of the sun gear; r is a radical of hydrogen 2 The rotation radius of the grid unit of the sun wheel; w is a 2 Is the angular velocity of the sun gear; n is a radical of an alkyl radical 2 The rotational speed of the sun gear;
w 3 ＝2πn 3 (6)
in formulas (5) to (7): f 3 A grid cell centrifugal force for the planet carrier; m is 3 The grid cell mass of the planet carrier; r is 3 The mesh unit rotating radius of the planet carrier; w is a 3 Is the angular velocity of the planet carrier; n is 3 The rotational speed of the planet carrier; z is a radical of formula 2 The number of sun gear teeth; z is a radical of formula R The number of teeth of the inner gear ring;
in equations (8) to (9): f 4 A grid cell centrifugal force that is a planetary gear; m is a unit of 4 A grid cell mass for the planetary gear; r is a radical of hydrogen 4 The revolution rotation radius of the grid unit of the planetary gear; w is a 4 Is the revolution angular velocity, w, of the planetary gear 4 ＝w 3 ；r 41 The mesh unit autorotation radius of the planet gear; w is a 41 Is the rotational angular velocity of the planetary gear; r is 4 The revolution radius of the central line of the planetary gear; r is 42 The pitch circle radius of the planet gear; r is 22 The pitch circle radius of the sun gear;
s9, adjusting all parts to an ideal assembly position:
adjusting each part in the step S1 to an ideal assembly position without considering the manufacturing error and the assembly error of the part;
s10, determining the 1 st meshing position of the planetary gear mechanism: rotating the planet gear to any rotational symmetry plane position of the inner gear ring to serve as a 1 st meshing position of the planet gear mechanism so as to calculate the load balancing coefficient of the planet gear mechanism at the moment and evaluate the reasonability of the structural design of parts;
s11, defining a calculation working condition: the calculation condition consists of the boundary condition in the step S4, the initial temperature in the step S5, the load 1 in the step S6, the load 2 in the step S7 and the load 3 in the step S8;
s12, carrying out finite element analysis: according to the calculation condition defined in the step S11, the tangential force of the spring unit of the simulated rolling needle in the revolution direction of the planetary gear is calculated in consideration of geometric nonlinearity;
s13, calculating the load sharing coefficient of the planetary gear mechanism at the 1 st meshing position:
multiplying the tangential force of each spring unit of the simulation needle roller in the revolution direction of the planetary gear by the revolution radius of the supported planetary gear to obtain the torque transmitted by the planetary gear shaft, and taking the ratio of the maximum value of the torque to the average value of all the torques as the load-sharing coefficient of the planetary gear mechanism at the meshing position 1, specifically see the calculation formula (10);
in equation (10): s 1 Is the load-sharing coefficient; f. of j The tangential force of the jth spring unit simulating the roller pin along the revolution direction of the planetary gear; r 4j The revolution radius of the planet gear supported by the jth spring unit;
s14, adjusting the gear meshing position of the planetary gear mechanism and calculating the load balancing coefficient of the corresponding position:
the planet gears are sequentially rotated to other non-rotational symmetry plane positions, simultaneously the sun gear and the planet carrier are rotated according to the speed ratio to obtain the 2 nd, the 3 rd, \8230the8230and the x-th meshing positions of the planet gear mechanism, the steps S11 to S13 are respectively repeated at each position, and the load-sharing coefficient S of the corresponding meshing position is calculated 2 、s 3 、……s x (ii) a Get s 1 、s 2 、s 3 、……s x The medium maximum value is used as the load-sharing coefficient of the planetary gear mechanism;
and S15, considering the manufacturing error and the assembly error of the parts, and repeating the steps S11 to S14 to calculate the load sharing coefficient of the planetary gear mechanism.
2. A method of calculating a load sharing factor of a planetary gear mechanism according to claim 1, characterized in that: in the step S1, a bearing rolling body is simplified and modeled by adopting a spring unit, for a bearing with an outer ring and an inner ring, nodes at two ends of the spring unit for simulating the rolling body are respectively connected to slave points of two RBE3 units, the two slave points are positioned on a geometric central line of the bearing, the slave point of one RBE3 unit selects a geometric center of an outer ring raceway, the master point selects a node on the outer ring raceway, the slave point of the other RBE3 unit selects a geometric center of an inner ring raceway, and the master point selects a node on the inner ring raceway; for a needle bearing without an outer ring and an inner ring, nodes at two ends of a spring unit simulating a needle are also connected to two RBE3 unit slave points, the two slave points are positioned on a geometric central line of the needle bearing, one slave point of one RBE3 unit selects one point on the central line of the needle bearing, a master point selects a grid node of a planetary gear part contacted with the outer diameter side of the needle bearing, the other slave point of the other RBE3 unit selects the other point on the central line of the needle bearing, and the master point selects a grid node of a planetary gear shaft part contacted with the inner diameter side of the needle bearing; the number of spring units is equal to the number of bearings.
3. A method of calculating a load sharing factor of a planetary gear mechanism according to claim 1, characterized in that: in the step S1, interference between the bearing and the shell and between the bearing and the supported part is not considered, and zero clearance fit is realized.
4. A method of calculating a load sharing factor of a planetary gear mechanism according to claim 1, characterized in that: s3, the spring unit stiffness K represents the comprehensive stiffness of all rolling bodies in a bearing, and the specific acquisition method is subdivided into the steps from S3-1 to S3-8;
s3-1, establishing a finite element model of a single rolling body: the method comprises the steps of carrying out meshing on three parts, namely a rolling body, an upper flat plate and a lower flat plate, wherein meshes of contact positions need to be finely divided so as to improve load transfer precision and deformation calculation precision; the upper flat plate and the lower flat plate are assumed to be rigid bodies so as to obtain the rigidity of a single rolling body; the parts are assembled together by defining a contact relation;
s3-2, defining the material property of the finite element model of the single rolling body: defining the elastic modulus E and the Poisson ratio mu of the rolling body;
s3-3, defining finite element model boundary conditions of a single rolling body: the boundary conditions include two types, namely, the lower flat plate is completely restrained and fixed; secondly, all the degrees of freedom of the upper flat plate except the normal degree of freedom are restrained so as to ensure that the upper flat plate can only move along the normal direction;
s3-4, applying load F borne by single rolling body 1 ：F 1 Acting on the upper plate, F 1 The rolling bodies are compressed and deformed along the normal direction of the upper flat plate;
s3-5, defining the calculation condition of a single rolling body: the calculated operating conditions include the boundary conditions in S3-3 and the load F in S3-4 1 ；
S3-6, carrying out finite element analysis on the single rolling body: calculating the compression deformation X of the rolling body according to the calculation conditions defined in the step S3-5 1 Which is equal to the load F 1 The distance of the action point moving along the normal direction of the upper flat plate;
s3-7, calculating the rigidity K of single rolling body 1 : rigidity K 1 See concretely the calculation formula (1);
s3-8, calculating the rigidity K of the spring unit: k is equal to the comprehensive rigidity of all rolling bodies in one bearing, and particularly, the calculation formula (2) is shown;
K＝K 1 ×(COSθ 1 +COSθ 2 +……+COSθ i ) (2)
in the formula, theta i The angle of the ith rolling body relative to the 1 st rolling body is taken as the center of a circle at the intersection point of planes formed by the central line of the bearing and the central points of all the rolling bodies, the 1 st ball can be any ball in the bearing, and theta is the angle between the ith rolling body and the 1 st rolling body 1 ＝0，θ i ＜90。
5. A method of calculating a load sharing factor of a planetary gear mechanism according to claim 4, characterized in that: the rigidity of the spring unit needs to be defined in the radial direction of the bearing by means of a cylindrical coordinate system, the origin of the cylindrical coordinate system is located on the central line of the bearing, the r axis of the coordinate system is in the radial direction of the bearing, the z axis is in the central line direction of the bearing, and t is determined by the r axis and the z axis according to the right-hand rule.
6. A method of calculating a load sharing factor of a planetary gear mechanism according to claim 1, characterized in that: in step S5, the initial temperature is defined as room temperature.
7. A method of calculating a load sharing factor of a planetary gear mechanism according to claim 1, characterized in that: in step S6, the high-temperature loads applied to all the part finite element models in step S1 are the same, and the temperature value is larger than the normal working temperature value of the planetary gear mechanism.
8. A method of calculating a load sharing factor of a planetary gear mechanism according to claim 1, characterized in that: in step S7, the torque M is the maximum design input torque of the planetary gear mechanism.
9. A method of calculating a load sharing factor of a planetary gear mechanism according to claim 1, characterized in that: in step S10 and step S14, the meshing positions included are uniformly distributed between two adjacent symmetry planes of the ring gear.
10. A method of calculating a load sharing factor of a planetary gear mechanism according to claim 1, characterized in that: s15, the manufacturing error is equivalent to a position error of one of the planetary gear central lines along the revolution tangent direction of the planetary gear, namely an equivalent tangential position error, which is shown in a calculation formula (11); the assembly error is equivalent to a position error of the central line of one of the planet gears along the revolution radius direction of the planet gears, namely an equivalent radial position error, and particularly see a calculation formula (12); the manufacturing error and the assembly error are applied to the planetary gear by adopting a comprehensive equivalent position error, the calculation of the comprehensive equivalent position error is shown in a formula (13), and specifically, the distance of the planetary gear deviating from an ideal assembly position by the comprehensive equivalent position error is used for evaluating whether the design of the planetary gear mechanism meets the requirements of the manufacturing process;
in equations (11) to (13): Δ w 1 Is an equivalent tangential position error; p is a radical of 1 Is the sun gear eccentricity error; p is a radical of 2 The eccentric error of the planet wheel; p is a radical of 3 Is the eccentric error of the inner gear ring; p is a radical of formula 4 The eccentric error of the planet carrier; p is a radical of 5 The eccentric error of the shaft hole of the planet gear shaft; theta is the gear pressure angle; Δ w 2 Is the equivalent radial position error; a is 1 An assembly error for the sun gear; a is 2 Assembling errors for the planet gears; a is 3 An assembly error of the inner gear ring; a is a 4 Assembly errors for the planet carrier; a is 5 The assembly error of the shaft hole of the planet gear shaft; Δ w is the integrated equivalent position error.
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| CN115577602A (en) * | 2022-11-24 | 2023-01-06 | 河北工业大学 | Wind power gear box load balancing test analysis method and system |
| CN116663328A (en) * | 2023-07-26 | 2023-08-29 | 河北工业大学 | Gear box load balancing characteristic calculation method, device, equipment and medium |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115577602A (en) * | 2022-11-24 | 2023-01-06 | 河北工业大学 | Wind power gear box load balancing test analysis method and system |
| CN116663328A (en) * | 2023-07-26 | 2023-08-29 | 河北工业大学 | Gear box load balancing characteristic calculation method, device, equipment and medium |
| CN116663328B (en) * | 2023-07-26 | 2023-10-20 | 河北工业大学 | Gear box load balancing characteristic calculation method, device, equipment and medium |
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